OMAL

If you are using the denim theme I know it works well when I tested it. Post a link and I can check it out.

Unfortunately, the website is under test domain so can't make it public.

I somewhat solved the issue. The main culprit is that sub-navigation's div is allocated at the bottom of the phone screen with position:absolute style, so overwriting the position property fixes the position.
But I still have an issue, that is ugly lag time when focus is out of the menu which has child menu. Child menu is still alive around 800 mili sec after loosing focus.
Do you know how to change the delay time to zero when focus is out?